1-Linear-regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.random.rand(100,1)\n",
    "y = 10 + 3 *   X + np.random.rand(100,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Data points to be used in this notebook')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,y)\n",
    "plt.title(\"Data points to be used in this notebook\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In linear regression we are trying to fit the best line to the data. Polynomial regression will not be covered here. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Normal Equation "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\theta^{min} = (X^TX)^{-1}X^Ty \\\\\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_temp = np.c_[np.ones((len(X),1)), X] #need this so we can get \"b\" back - adds column of 1s to the left\n",
    "theta_min = np.linalg.inv(X_temp.T.dot(X_temp)).dot(X_temp.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10.47364245],\n",
       "       [ 2.92442516]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = np.c_[np.ones((2,1)), X_new]\n",
    "y_pred = X_new_b.dot(theta_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10.47364245],\n",
       "       [16.32249276]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X,y,\"b.\")\n",
    "plt.plot(X_new, y_pred, \"g-\")\n",
    "plt.axis([0, 1, 10, 15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.  Batch Gradient Descent "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean squared error is a convex function so using batch gradient descent will guarantee reaching the global minimum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loss function\n",
    "\n",
    "$$\n",
    "MSE = \\frac{1}{m}\\sum_{i = 1}^{m}(y_{i}-y_{i}^{pred})^2 \\\\\n",
    "$$\n",
    "\n",
    "Cost function\n",
    "\n",
    "$$\n",
    "\\frac{\\partial}{\\partial \\theta_{j}}MSE(\\theta) = \\frac{2}{m}\\sum_{i = 1}^{m}(\\theta^{T}x^{(i)} - y^{(i)})x_{j}^{(i)}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\nabla_{\\theta}MSE(\\theta) = \\frac{\\partial}{\\partial \\theta_{0}}MSE(\\theta)...\\frac{\\partial}{\\partial \\theta_{m}}MSE(\\theta) = \\frac{2}{m}X^{T}(X\\theta-y)\\\\\n",
    "$$\n",
    "\n",
    "Step function\n",
    "\n",
    "$$\n",
    "\\theta^{next} = \\theta - \\alpha\\nabla_{\\theta}MSE(\\theta)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.5\n",
    "theta = [[0],\n",
    "        [0]] #can be done, unlike in nerual networks\n",
    "iteration_count = 30\n",
    "X_temp = np.c_[np.ones((len(X),1)), X]\n",
    "progress = []\n",
    "\n",
    "for i in range(iteration_count):\n",
    "    gradients = 2/len(X) * X_temp.T.dot(X_temp.dot(theta) - y)\n",
    "    progress.append(np.abs(gradients[0][0]) + np.abs(gradients[1][0]))\n",
    "    theta = theta - alpha * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10.3589391 ],\n",
       "       [ 3.14678941]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(progress)\n",
    "plt.xlabel(\"Epoch\")\n",
    "plt.ylabel(\"MSE\")\n",
    "plt.title(\"Training details\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = np.c_[np.ones((2,1)), X_new]\n",
    "y_pred = X_new_b.dot(theta)\n",
    "\n",
    "plt.plot(X,y,\"b.\")\n",
    "plt.plot(X_new, y_pred, \"g-\")\n",
    "plt.axis([0, 1, 10, 15])\n",
    "plt.title(f\"Alpha: {alpha} iterations: {iteration_count}\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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